论文标题
角色总和仿射空间和应用
Character sums over affine spaces and applications
论文作者
论文摘要
给定一个有限字段$ \ MATHBB f_q $，一个正整数$ n $和$ \ Mathbb f_q $ -Affine Space $ \ Mathcal a \ subseteq \ subseteq \ Mathbb f_ {q^n} $，我们在sum $ $ $ \ sum_ {a a \ in \ mathcal a $ y $ $ a $ a} $ a $ a $ a $ a $ a $ a）上提供了一个新的限制$ \ mathbb f_ {q^n} $。我们专注于估计对$ \ mathbb f_ {q^n} $存在的特殊原始元素的结果的适用性。特别是，我们可以对以前的作品进行实质性改进。
Given a finite field $\mathbb F_q$, a positive integer $n$ and an $\mathbb F_q$-affine space $\mathcal A\subseteq \mathbb F_{q^n}$, we provide a new bound on the sum $\sum_{a\in \mathcal A}χ(a)$, where $χ$ a multiplicative character of $\mathbb F_{q^n}$. We focus on the applicability of our estimate to results regarding the existence of special primitive elements in $\mathbb F_{q^n}$. In particular, we obtain substantial improvements on previous works.
